2013/03/26 by Alejandro M. F Rivas, Alejandro M F Rivas · 1 citation
Mathematics · Physics and Astronomy · #Chaotic #Invariant (physics) #Linearization #Matrix (chemical analysis) #Matrix function #Phase space #Propagator #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Semiclassical physics #Spectral Theory in Mathematical Physics #math.DS #nlin.CD #quant-ph
paper · pdf · doi:10.1088/1751-8113/46/14/145101
published in Journal of Physics A Mathematical and Theoretical 46(14), 145101 (Institute of Physics) · 20 pages, no figures. arXiv admin note: text overlap with arXiv:quant-ph/0612220
openalex publication_date 2013/03/26 · arxiv created 2013/06/17 · arxiv updated 2013/06/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A semiclassical approximation for the matrix elements of a quantum chaotic propagator in the scar function basis has been derived. The obtained expression is solely expressed in terms of canonical invariant objects. For our purpose, we have used the recently developed, semiclassical matrix elements of the propagator in coherent states, together with the linearization of the flux in the neighborhood of a classically unstable periodic orbit of chaotic two-dimensional systems. The expression derived here is successfully verified to be exact for a (linear) cat map, after the theory is adapted to a discrete phase space appropriate to a quantized torus.